INSTALMENT WARRANT MECHANICS
´
Antonie A. Kotze
Financial Chaos Theory†
consultant@quantonline.co.za
Abstract
Instalment warrants are very popular in Australia and these instruments have been
listed by Nedbank and Standard Bank in South Africa.
Instalments are ﬁnancial products, that allow investors to gain direct exposure to
shares by making a part payment upfront and delaying an optional ﬁnal payment (or
second instalment) until a later date (expiry date). This allows an investor to buy
shares, and other securities, for a fraction of the current share price whilst receiving
the beneﬁts of capital growth and ordinary dividends.
November 2010
†
Financial Chaos Theory is a consulting ﬁrm specialising in ﬁnancial derivatives. Surf to
www.quantonline.co.za.
1 What are Instalments?
In simple terms, an instalment is a loan to buy shares. Instalments will enable you to either
make a new investment that gives you exposure to shares of your choice, or you can borrow
against shares you already own, releasing cash for other investments.
Either way, the loan amount can be repaid at any time until the instalment matures,
however it is important to note that repayment is not compulsory. If the share price falls
you do not have to repay the loan and you will not be subject to margin calls.
Essentially, a loan is created which reﬂects the value of the second instalment (or exercise
price). When you buy an instalment you will also pay an interest amount for the loan and
a borrowing fee.
Holders will generally be entitled to any distributions (dividends) that are paid on the
underlying share. There is a diﬀerence between the instalments oﬀered by Nedbank and
Standard Bank. The diﬀerence is that the Nedbank instalments pay out the full dividend.
So on the ex-dividend date the share instalment will drop in Rand terms by the full divi-
dend amount and the investor will receive it in cash. The Standard Bank instalments are
discounted in that you do not get the dividend so ex-dividend day will have no eﬀect on the
price of the share instalment.
To understand the pricing of an instalment warrant, we have to understand put-call-
parity. This is explained next.
2 Put-Call-Parity
Put-call parity is a relationship that exists between the prices of European put and call
options where both have the same underlier, strike price and expiry date [Hu 06]. This
relationship is derived using arbitrage arguments [Ko 02]. Consider two portfolios consisting
of
• A call option and an amount of cash equal to the present value of the strike price.
• A put option and the underlier.
In Figure 2 we compare the expiration value for these two portfolios, with x representing the
common strike price.
What is signiﬁcant about Figure 2 is the fact that the two portfolios (call + cash and
put + underlier) have identical expiration values. Irrespective of the value of the underlier
at expiration, each portfolio will have the same value as the other.
1
Figure 1: Put-Call Parity: Portfolios have Identical Expiration Values
A portfolio comprising a call option and an amount of cash
equal to the present value of the option’s strike price has
the same expiration value as a portfolio comprising the
corresponding put option and the underlier. For European
options, early exercise is not possible. If the expiration values of
the two portfolios are the same, then their present values must also
be the same. This equivalence is put-call parity. See [Risk].
If the two portfolios are going to have the same value at expiration, then they must have
the same value today. Otherwise, an investor could make an arbitrage proﬁt by purchas-
ing the less expensive portfolio, selling the more expensive one and holding the long-short
position to expiration. Accordingly, we have the price equality
c + P V (x) = p + s (1)
where
• c = the current market value of the call;
• P V (x) = the present value of the strike price x, discounted from the expiration date
at a suitable risk free rate r (here in continuous format);
2
• p = the current market value of the put;
• s = the current market value of the underlier.
Equation (1) is the put-call parity relationship. Note that it is not based on any option
pricing model. It was derived purely using arbitrage arguments. It applies only to European
options, since a possibility of early exercise could cause a divergence in the present values of
the two portfolios.
Put-call parity oﬀers a simple test of option pricing models. Any option pricing model
that produces put and call prices that do not satisfy put-call parity must be rejected as
unsound. Such a model will suggest trading opportunities where none exist.
Alternatively, consider the following 2 portfolios
Figure 2: Put-Call Parity in portfolio format
Payoﬀs A and B in Figure 2 are the same and the risk is the same, hence the costs of A
and B must be equal, i.e.
c = S0 e−dT + p − Xe−rT (2)
⇒ c − p = S0 e−dt − Xe−rT
Equation (2) is general and the put-call-parity relationship here includes a dividend yield d.
3 The Instalment Warrant
From equation (2) and portfolio (A) in Figure 2 we see that we can replicate a long call with
the following trades:
1. Buy the stock at S (take future dividend payments into account if necessary)
3
2. Buy a put with a strike at X
3. To do this, you have to borrow an amount Xe−rT
What will actually happen
1. client buys share at S
2. client pays 50% of this and borrows the other 50%. Client pays interest on this.
3. client buys a put at a strike that is lower than the share price (usually 50% of the share
price1 on the issue date). After listing of instrument this strike remains ﬁxed for the
life of the instalment.
4 Pricing an Instalment Warrant
Let the following hold:
S is the current share price;
S0 is the share price on the date of issue;
d is the current dividend yield of the share in NACA format;
α is the instalment multiplier or conversion ratio
K is the strike price given by
K = α S0 .
Now, the pricing of an instalment is
V = S + P (K) − P V (3)
where P is the put with a strike price of K and P V is the present value of the loan to the
investor given by
K
PV =
(1 + r)t
with r the loan rate to the investor in NACA format and t the time till expiry.
S is given by the following
S if dividends are given back to investor
S = S
if dividends are NOT given back to investor
(1+d)t
Equation (3) is just the put-call-parity relationship given in Equation (2).
1
Instalments can have strike prices that are up to 90% of the share price. These are called “hot” instal-
ments.
4
5 Funding Instalment Warrant
An investor that buys an instalment warrant buys a synthetic call option at a strike K. The
question is, can the opposite be done? Can an investor buy a synthetic put using the above
methodology? The answer is yes.
From equation (2) we can rewrite put-call-parity as follows
p = c + Xe−rT − S0 e−dT (4)
During a trade, where we incorporate this methodology, the investor would
1. sell the share at S
2. receive 50% of this and deposit the other 50% with issuer. Investor receives interest
on this.
3. buy a call at a strike that is higher than the share price (usually 50% above the share
price on the issue date). After listing of instrument this strike remains ﬁxed for the
life of the instalment.
If the investor owns the shares, this method allows him/her to raise cash with the shares
as collateral. The issuer can have a scrip lending agreement and on-lend the shares to the
investor. The scrip lending cost is then incorporated into the valuation of this instrument.
Pricing is similar to that given by Equation (3) but changed slightly to
V = P V + C(K) − S + S δ
with δ the scrip lending fee as a percentage if applicable.
6 Two Other Instruments
Using put-call-parity we can create instruments whereby investor synthetically short war-
rants. Rearranging equation (2) gives us
−C(K) = −P (K) + P V − S + S δ − short call
or
−P (K) = −C(K) − P V + S − short put.
7 Proﬁts on Instalments
Proﬁt on instalment warrants are made in a similar manner to proﬁts on ordinary warrants
i.e., through
1. the bid-oﬀer spread;
5
2. buying the volatility wholesale and selling it at retail levels
3. delta hedging.
There is an extra factor though, the interest at which the investor borrows the money from
the issuer — the interest rate spread is always in favour of the issuer.
References
[Hu 06] J. Hull, Options, Futures, and other Derivatives, 6th Edition, Pearson International
Edition (2006)
e
[Ko 02] A. A. Kotz´, Equity Derivatives: eﬀective and practical techniques for mastering
and trading equity derivatives, Workshop proceedings (2002)
[Risk] Riskglossary.com at http://www.riskglossary.com/link/put call parity.htm
There are some excellent web resources like
• http://203.15.147.66/products/pdf/instalment warrants getting started.pdf
• http://thebull.com.au/experts/a/291-what-are-the-pros-and-cons-of-
instalment-warrants.html
• https://www.warrants.standardbank.co.za/warrants/nsp/ContentManagement/
DocumentDownloadPage.aspx?documentDownloadPageId=1
Disclaimer
This publication is conﬁdential, intended for the information of the addressee only and may not be
reproduced in whole or in part in any manner whatsoever, nor may copies be circulated or disclosed to any
other party, without the prior written consent of Financial Chaos Theory (Proprietary) Limited (“FCT”).The
report and any information which may have been given orally by any director, other oﬃcer or duly authorised
employee of FCT is based on information from sources believed to be reliable, but is not guaranteed as to
accuracy or completeness. FCT, its aﬃliates, directors and other oﬃcers disclaim any responsibility for
any acts or omissions arising as a result of any of the information gleaned from this report and/or for any
loss occasioned in any manner whatsoever in consequence of the information herein contained. Neither this
report nor any opinion expressed herein should be considered as an oﬀer or allocation of an oﬀer to sell or
acquire any securities mentioned. FCT, its aﬃliates, directors and oﬃcers reserve the right to hold positions
in securities mentioned in this publication and further reserve the right from time to time to provide or oﬀer
advisory ﬁnancial services for or to receive such services from any company mentioned in this report.
6